Can you experience slight tingling in arm from tennis elbow?

Possibly: By definition, tennis elbow is a tendon problem on the outside of the elbow. Tingling suggests nerve inflammation. There are small nerves near the tendon that can get inflamed at the same time. Another cause could be nerve irritation of the nerve from the neck. The C7 nerve, if inflamed, will often refer pain to the outside of the elbow. The radial nerve can get inflamed/compressed near the elbow.